If you're in-state and want to do Patent Prosecution in DC, I'd go to GMU over GW. If you're out of state, if you can get into GW, you might be able to get a scholly at GMU.

If you're interested in patent litigation, I'd probably take GW, because they have more biglaw firms with patent litigation groups that come to interview on campus. However, litigation is quite selective, and if you don't have decent grades at any school, you'll be shut out.